# Spring 2018

Faculty Organizers: Professors Thomas Johnstone and Johann Thiel

Room and Time: N719, 12:45-2pm

Schedule:

 February 1 No meeting 8 Speaker: Brad Isaacson 15 No meeting (club fair) 22 Speaker: Satyanand Singh
 March 1 No meeting 8 Speaker: Thomas Johnstone 15 Speaker: Arthur Kramer 22 Speaker: Johann Thiel 29 Speaker: Viviana Acquaviva
 April 5 No Meeting 12 No Meeting 19 Speaker: Ezra Halleck 26 Speaker: Ezra Halleck
 May 3 No Meeting 10 17 No Meeting

Abstracts — Spring 2018

Date: February 8, 2018
Title: Let’s Play Sudoku!
Abstract: Sudoku is a very popular number puzzle.  In this talk, we will discuss some of the strategies for playing Sudoku, including naked and hidden pairs/triples, unique rectangles, and alternating inference chains.  May there never again be a Sudoku puzzle that you are unable to solve.

Date: February 20, 2018
Speaker: Dr. Satyanand Singh (NYCCT)
Title: Making the Perfect Billiard Shot
Abstract: Come sharpen your billiard skills with the help of tools from elementary geometry. This fun presentation will show you how to make a perfect shot. This talk is accessible to students with a basic knowledge of algebra and trigonometry.

Date: March  8, 2018
Speaker: Dr. Thomas Johnstone (NYCCT)
Title: Is the product of any k many consecutive integers always divisible by k factorial?
Abstract: Recall that “k factorial” is defined as the product of all integers between 1 and k, inclusive. There are many examples when the product of k many consecutive integers is divisible by k factorial. For instance, if k=5, then the product of the five consecutive integers 12, 13, 14, 15, 16 is divisible by five factorial: indeed, 12*13*14*15*16=524160, which is divisible by 1*2*3*4*5=120.
In this talk, we will answer the question whether the product of k many consecutive integers is always divisible by k factorial. While this question can be answered using combinatorial arguments, we shall rely on elementary number-theoretic arguments such as basic divisibility rules only.

Date: March 15, 2018
Speaker: Dr. Arthur Kramer (NYCCT)
Title: Numbers: Real vs Imaginary
Abstract: Imaginary numbers are as “real” as real numbers. Many of the greatest minds did not fully accept imaginary numbers as “real” mathematical quantities. It took a brilliant engineer to see in them as an elegant application to solving the problems of ac electricity. Such is the story with many scientific discoveries. Prof. Kramer will explore numbers and the evolution of imaginary numbers, the intriguing history surrounding them and their eventual acceptance as a “real” number system by the scientific community.

Date: March 22, 2018
Speaker: Dr. Johann Thiel (NYCCT)
Title: Roulette Wheel Betting
Abstract: A typical American roulette wheel has 38 different pockets. Two are colored green while the other 36 are split evenly between black and red. One way to bet on the roulette wheel is to bet on the color (black or red) of the next spin. The payout for this kind of bet is 1-to-1.
If we start out with \$30 and want to try to double our money (or lose it all trying), what betting strategies can help improve our odds? What does this have to do with matrices? We will try to answer these questions and more in this introductory talk.

Date: March 29, 2018
Speaker: Dr. Viviana Acquaviva (NYCCT)
Title: The science of machine learning
Abstract: Machine learning is the discipline of teaching computers to recognize, classify and predict relationships within data. It has countless applications in the most diverse fields: it can be used to generate to recommend movies and articles, to generate poems in the style of Shakespeare, to accelerate diagnoses of dangerous diseases, to prevent insurance fraud, to improve system security, and many other endeavors. At their core though, machine learning algorithms are just a set of clever mathematical tools that allow us to re-map complicated questions onto simpler optimization problems. We discuss our ID course, Machine Learning for Physics and Astronomy, in which we use data sets from Physics and Astronomy and Python programming to learn machine learning from the ground up. We present a selection of algorithms to solve challenges such as discovering new elementary particles, finding dark energy, identifying variable stars, and understanding the origin of galaxy shapes.

Date: April 19, 2018
Speaker: Dr. Ezra Halleck (NYCCT)
Title: Statistical Mechanics and Combinatorics
Abstract: In this picture-rich and proof-light treatment, I will begin with the connections between the 2 subjects but focus on enumerative and bijective aspects. One example is tiling using dimers. Another is a model of ice, again in a plane. There will be several hands-on activities as well as recursive programming examples in MATLAB, Python and R.

Date: April 26, 2018
Speaker: Dr. Ezra Halleck (NYCCT)
Title: A 2-Dimensional Model for Ice and Alternating Sign Matrices
Abstract: In the later part of the 20th century, physicists developed the Ising and Potts models for ice and interacting spins on a crystalline lattice. Mathematicians noticed connections to several constructs, including the alternating sign matrices illustrated above. There was much interest on the growth of these objects as the size increased. A conjecture on an exact count for a given size quickly arose. Finding a proof was a hot problem for years, with many discrete mathematicians adding pieces towards its proof. Doron Zielberger put in the final piece in 1995.
This picture-rich and proof-light treatment will begin with the bijection between the model and the matrix illustrated above but then focus on enumerative aspects of the matrix class. There will be several hands-on activities.